The Serbian midfielder failed to win a trophy during his five-year spell at Old Trafford but insists that it doesn't detract from his experience at one of the biggest clubs in world football.
Matic told FourFourTwo magazine: "I don't cry for the past. It was my dream to win the league with United - it didn't happen. The closest we got to a trophy was in the Europa League final against Villarreal, as well as an FA Cup final with Chelsea. But that doesn't change my perspective on United now - I'm proud of the time I spent there."
Matic was at the club when Cristiano Ronaldo made his much-hyped return to United in 2021 and is pleased to have had the opportunity to share a dressing room with footballing icon.
He said: "I was very happy to share a dressing room with him, play with him, and learn new things from him every day.
"It was a special moment when he returned. You could feel the pressure when he was there - I saw the young guys always try to give him the ball, even when it wasn't the right pass.
"He was a fantastic person, always positive - he didn't want to be negative at any point, which is probably why he's achieved what he has in his career. He wasn't in his prime, but I'm proud to have played with him."
Matic's former manager Jose Mourinho described United's second-place finish in the 2017-18 Premier League campaign as one of the finest achievements of his career and the midfielder can "understand" why the coach made the comment.
Matic - who now plays for Italian side Sassuolo - said: "I understand why he said that. I wanted to be a champion at United and believed we could do more. Second wasn't bad, but we should have won the title.
"United must forget about commercial things and become a football club again."